Mathematical Definitions
For a given real field, we can say that the theory has a mass gap if the two-point function has the property
with being the lowest energy value in the spectrum of the Hamiltonian and thus the mass gap. This quantity, easy to generalize to other fields, is what is generally measured in lattice computations. It was proved in this way that Yang-Mills theory develops a mass gap. The corresponding time-ordered value, the propagator, will have the property
with the constant being finite. A typical example is offered by a free massive particle and, in this case, the constant has the value 1/m2. In the same limit, the propagator for a massless particle is singular.
Read more about this topic: Mass Gap
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